Suppose we roll two fair six-sided dice, one red and one blue. Let A be the event that the two dice show the same value. Let B be the event that the sum of the two dice is equal to 12. Let C be the event that the red die shows 4. Let D be the event that the blue die shows 4.
(a) Are A and B independen
(b) Are A and C independent?
(c) Are A and D independent?
(d) Are C and D independent?
(e) Are A, C, and D all independent?